What is a Galaxy?
Friday, October 10
Next Planetarium Show: Wed, Oct 15
Are stars distributed uniformly through
space, or do they clump together?
Astronomers now know that stars
are in clumps called “galaxies”. To
find that out, they had to know
how stars are distributed in 3-D.
Finding Sun’s distance is relatively easy.
Bounce a radio signal from Venus.
Round trip travel time ÷ 2 = One-way travel time.
One-way travel time × c = distance to Venus.
c = speed of light
Once you’ve plotted the
orbit of Venus, you know
where the Sun is: at a
focus of the elliptical orbit.
average Earth-Sun distance =
1 astronomical unit (AU) =
149,597,870.69 kilometers
Most stars are unresolved in angle.
Seen by a human eye, they’re
blobs an arcminute across;
resolution of eye = 1 arcminute.
Seen with a large telescope, they’re
blobs an arcsecond across;
resolution of telescope = 1 arcsecond.
A star (like the Sun) will be 1/2° across
when its distance is 115 times its diameter.
A star will be an arcsecond across when
its distance is 206,000 times its diameter.
Because stars are unresolved,
we know they are far away.
“Far away” = at a distance larger than
206,000 times the diameter of a star.
206,000 × Sun’s diameter =
290 billion kilometers =
11 light-days
Can we actually find the distance?
Yes! We can find the distance to nearby
stars by measuring their parallax.
Parallax = shift in apparent position of star
over the course of half a year.
Remember: the parallax is too small to be
seen by the naked eye (< 1 arcminute).
For the closest stars, the parallax is large
enough to be measured with a telescope.
In 1838, F. W. Bessel found
a parallax of 0.3 arcseconds
for a nearby star.
How to find distance by measuring parallax:
Parallax and distance are related by a
simple equation.
1
d
p
p = parallax of star (in arcseconds)
d = distance to star (in parsecs)
1 parsec = distance at which a star has a parallax
of 1 arcsecond = 206,000 AU = 3.26 light-years.
How far is the
journey from here to
Proxima Centauri?
1
1
d 
 1.3 parsecs
p 0.77
= 4.2 light-years = 270,000 AU
The Parallax Problem
Best parallax measurements
were provided by the
Hipparcos satellite.
Parallaxes < 1/1000 of an arcsecond
were too small to measure.
Distances > 1000 parsecs can’t be
found from parallax.
How can we find the distance to a star
more than 1000 parsecs away?
Use the “World-Famous
Inverse-Square Law”.
The Inverse-Square Law.
Every star has a luminosity (L):
this the wattage of the star (how
much energy it emits per unit time).
40 watts
26
4×10 watts
We don’t measure the luminosity of a star.
We measure the flux (f):
the
wattage collected per unit area.
Flux of sunlight at the
Earth’s location =
1400 watts per square meter
The flux is related to the luminosity
by an inverse-square law.
What is the flux f
at a distance r
from a star of
luminosity L?
At a distance d from the star, the luminosity
L is spread over an area 4 π r2.
f
L
4 r
2
Flux goes inversely as the square of distance.
What the %$*&@ does this have to
do with finding distances to stars??
If you know the luminosity L,
and you measure the flux f,
you can compute the distance r:
f
L
4 r
2
r
L
4 f
An object whose luminosity
you know is called a
“standard candle”.
Alas! Stars have a wide range
of luminosities.
Betelgeuse = high luminosity
Sun = medium luminosity
Proxima Centauri = low luminosity
For nearby stars, we can measure
distance (from parallax) and flux.
We compute luminosity:
L  4 r f
2
Eureka! Stars with identical spectra
have identical luminosity!
Spectra of stars
very hot & luminous
cool & less luminous
Find a star with a spectrum
identical to the Sun’s (for instance).
Measure the star’s flux f.
Assume the star’s luminosity is the
26
same as the Sun’s (L = 4 × 10 watts).
Compute the star’s distance:
r
L
4 f
We live in a disk-shaped
galaxy. The luminous
path called the “Milky
Way” is seen when we
look the long way
through the disk.
If we could see the Milky Way
galaxy edge-on from outside:
= 8000 parsecs
= 26,000 light-years
=1.7 billion AU
Other disk-shaped galaxies exist:
Andromeda Galaxy:
2 million light-years away
= 700,000 parsecs away
= 140 billion A.U. away
Galaxies
come in many
shapes
What is a galaxy?
A gravitationally bound assembly of
many stars (+ associated planets)
interstellar gas (+ dust)
and dark matter.
“many” ≥ 10 million
Monday’s Lecture:
Gravity for Beginners
Reading:
Chapter 4